Biophysical theory regards the electrophysiological interaction between passive and active patches of nerve membrane as functionally significant. Important examples include dendritic spines with both passive and excitable spine head membrane, myelination, and the interaction between dendrite and axonal membrane. The aim of this project is to explore, using mathematical modeling, analysis, and numerical computation the functional implications of these interactions. Last year we expanded our research efforts to include a new class of excitability problems involving a slowly-varying control parameter. We are pleased to report that this study revealed some new and valuable insights into the biophysical phenomena of accommodation. Areas of research initiated this year include the evaluation and study of the dynamics of an alternative mathematical model of the Hodgkin-Huxley squid data and applications of cable theory to assist experimenters in understanding the function of the first synapses in the visual system.